Melanin ablation guided by stepwise multi-photon activated fluorescence

ABSTRACT

A method and system of ablating melanin are provided. Stepwise multi-photon fluorescence is induced in melanin within a region of tissue. The fluorescence is detected, and at least a portion of the melanin from which the fluorescence is detected is ablated. The system and method can use a continuous wave laser in the near infrared range for the inducement and ablation of melanin, providing high resolution at low cost.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. Provisional Application No.62/020,459 filed 3 Jul. 2014, and to PCT Application No.PCT/US2015/038941, filed 2 Jul. 2015, and is a divisional application ofU.S. application Ser. No. 15/323,475, filed 3 Jan. 2017. Each of theaforementioned applications is hereby incorporated by reference in itsentirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

N/A

BACKGROUND

Melanin, a ubiquitous biological pigment produced by melanocytes in mostorganisms, is an important component of animal pigmentary systems.Naturally occurring pigmentation that determines hair, eye and skincoloration is attributed to two types of melanin: eumelanin andpheomelanin. Eumelanin is the dominant component of brown and blackpigments in dark skin and black hair, while pheomelanin is more commonin yellow and red pigments in hair. Melanin has not been wellunderstood, as it is an insoluble polymer without a well-definedstructure, which makes it difficult to isolate and study.

Melanin is related to many skin diseases, such as malignant melanoma,the most aggressive skin cancer; vitiligo, a disease characterized bythe loss of melanin pigment; melasma, an acquired brown hypermelanosisof the face; solar lentigines and ephelides, benign pigmented spots thatare associated with an increased risk of skin cancer; and nevus of Ota,a syndrome comprising a grayish-blue, macular discoloration affectingthe sclera of an eye and the ipsilateral facial skin in the area of thedistribution of the corresponding trigeminal nerve.

Selective photothermolysis has been widely used for treatments ofmelanin-related skin diseases. This technique utilizes nanosecond-domainlaser pulses to selectively ablate melanin and melanin-related cells.Despite its effectiveness, photothermolysis lacks the ability to targetindividual melanin particles, which limits its usage in treating skindiseases in some sensitive regions, such as nevus of Ota around the eye.

SUMMARY OF THE INVENTION

The invention relates to a method and system for ablation of melaninguided by the stepwise multi-photon activation of melanin in a region oftissue. A method of ablating melanin includes the steps of inducing thestepwise multi-photon fluorescence in melanin within the region oftissue, detecting the fluorescence from the melanin, and ablating atleast a portion of the melanin from which the fluorescence is detected.

The method and system can achieve high resolutions to ablate melaninwith no or minimal collateral damage to surrounding tissue. The methodand system are useful for treating a variety of melanin-related diseasesand conditions in human and non-human subjects.

Other aspects of the method and system include the following:

1. A method of ablating melanin comprising:

inducing stepwise multi-photon fluorescence in melanin within a regionof tissue;

detecting the fluorescence from the melanin in the region; and

ablating at least a portion of the melanin from which the fluorescenceis detected.

2. The method of item 1, wherein the step of inducing fluorescence inthe melanin comprises transmitting a beam of laser light from acontinuous wave laser source to the region of tissue to activatefluorescence from the melanin within the region.

3. The method of item 2, wherein a wavelength of the laser light rangesfrom 600 nm to 2 μm.

4. The method of any of the preceding items, wherein the beam of laserlight is scanned across an image plane.

5. The method of any of the preceding items, wherein the beam of laserlight is scanned across multiple image planes, each image plane locatedat a different depth within the region of tissue.

6. The method of any of the preceding items, wherein the beam of laserlight penetrates the region of tissue to a depth between a surface and500 μm.

7. The method of any of items 1-5, wherein the beam of laser lightpenetrates the region of tissue to a depth between a surface and 6 mm.

8. The method of any of items 1-5, wherein the beam of laser lightpenetrates the region of tissue to a depth of at least 6 mm.

9. The method of any of items 1-5, wherein the beam of laser lightpenetrates the region of tissue to a full depth of a dermis layer.

10. The method of any of the preceding items, wherein the fluorescenceis induced by irradiating the melanin in an image plane with radiationat a first intensity; and

the melanin is ablated by irradiating at least a portion of the melaninin the image plane with radiation at a second intensity greater than thefirst intensity.

11. The method of any of the preceding items, wherein the fluorescenceis induced by irradiating the melanin in an image plane with radiationat an intensity on the order of 10⁵ W/cm² to 10⁷ W/cm².

12. The method of any of the preceding items, wherein the fluorescenceis induced by irradiating the melanin with radiation at a first powerlevel; and

the melanin is ablated by irradiating the melanin with radiation at asecond power level greater than the first power level.

13. The method of any of the preceding items, wherein the step ofdetecting the stepwise multi-photon fluorescence includes generating amap of the detected fluorescence, the map comprising a series of imageplanes, each image plane comprising a pixel array in which pixels wherefluorescence has been detected are identified.14. The method of any of the preceding items, wherein:

the step of inducing the stepwise multi-photon fluorescence comprisesscanning a light source over the region of tissue,

the step of detecting the fluorescence from the melanin in the regioncomprises generating a map specifying areas of the detected fluorescencein the region, and

the step of ablating at least a portion of the melanin from which thefluorescence is detected comprises moving a light source over the regionof tissue to the areas of the detected fluorescence specified in themap.

15. The method of any of the preceding items, further comprisingrepeating, at a new region of tissue, the steps of inducing stepwisemulti-photon fluorescence in melanin, detecting the fluorescence fromthe melanin, and ablating at least a portion of the melanin from whichthe fluorescence is detected.16. The method of any of the preceding items, further comprisingmonitoring fluorescence from the region after ablation to determinecompletion of ablation.17. The method of any of the preceding items, wherein the fluorescenceis detected at a resolution of less than 10 μm in an image plane.18. The method of any of the preceding items, wherein the fluorescenceis detected at a resolution of less than 1 μm in an image plane.19. The method of any of the preceding items, wherein the fluorescenceis detected at a resolution of less than 500 nm in an image plane.20. The method of any of the preceding items, wherein the fluorescenceis detected at a resolution of a diameter of a single grain of melanin.21. The method of any of the preceding items, wherein the step ofablating the melanin comprises transmitting a beam of laser light from acontinuous wave laser source to the region of tissue to ablate at leasta portion of the melanin within the region.22. The method of any of the preceding items, wherein a wavelength ofthe laser light ranges from 600 nm to 2 μm.23. The method of any of the preceding items, wherein the beam of laserlight is moved over a trajectory in an image plane to ablate at least aportion of the melanin in the image plane.24. The method of any of the preceding items, wherein the beam of laserlight is moved over multiple image planes, each image plane located at adifferent depth within the region of tissue, to ablate at least aportion of the melanin in each of the multiple image planes.25. The method of any of the preceding items, wherein the beam of laserlight penetrates the region of tissue to a depth between a surface and500 μm.26. The method of any of items 1-24, wherein the beam of laser lightpenetrates the region of tissue to a depth between a surface and 6 mm.27. The method of any of items 1-24, wherein the beam of laser lightpenetrates the region of tissue to a depth of at least 6 mm.28. The method of any of items 1-24, wherein the beam of laser lightpenetrates the region of tissue to a full depth of a dermis layer.29. The method of any of the preceding items, wherein the melanin isablated at a resolution of less than 10 μm in an image plane.30. The method of any of the preceding items, wherein the melanin isablated at a resolution of less than 1 μm in an image plane.31. The method of any of the preceding items, wherein the melanin isablated at a resolution of less than 500 nm in an image plane.32. The method of any of the preceding items, wherein the melanin isablated at a resolution of a single grain of melanin.33. The method of any of the preceding items, wherein the step ofablating the melanin comprises ablating all the melanin in the region oftissue.34. The method of any of the preceding items, wherein in the steps ofinducing fluorescence and ablating the melanin, the region of tissue ishuman skin.35. The method of any items 1-33, wherein in the steps of inducingfluorescence and ablating the melanin, the region of tissue is non-humananimal skin.36. The method of any of the preceding items, wherein, in the step ofablating the melanin, the melanin is ablated without damage tomelanocytes present in the region of tissue.37. A method of treating a melanin-related disease or conditioncomprising:

performing the method of item 1, wherein the region of tissue is presentin a subject in need thereof.

38. The method of item 37, wherein the melanin-related disease orcondition is selected from the group consisting of melanocytic lesion,congenital or acquired hyperpigmentation or melanin deposition, andother skin discoloration from melanin deposition.

39. A method of lightening skin pigmentation comprising:

performing the method of item 1, wherein the region of tissue is presentin skin of a subject in need thereof.

40. A method of hair removal comprising:

performing the method of item 1, wherein the region of tissue is presentin a hair shaft of a subject in need thereof.

41. A system for ablating melanin comprising:

an objective lens assembly disposed on an optical path to focus light onan image plane within a region of tissue including melanin;

a first light source disposed to transmit a first light beam on theoptical path to the image plane within the region of tissue, the firstlight beam comprising a wavelength sufficient to induce step-wisemulti-photon fluorescence of melanin in the image plane;

a detector disposed to receive a step-wise multi-photon fluorescencesignal from the melanin in the image plane returning along at least aportion of the optical path; and

a second light source disposed to direct a second light beam on theoptical path to the image plane within the region of tissue, the secondlight beam comprising a wavelength sufficient to ablate melanin in theimage plane within the region of tissue.

42. The system of item 41, wherein the first light source comprises acontinuous wave laser source.

43. The system of items 41-42, wherein the second light source comprisesa continuous wave laser source.

44. The system of any of items 41 or 43, wherein the first light sourcecomprises a pulsed laser source.

45. The system of any of items 41, 42 or 44, wherein the second lightsource comprises a pulsed wave laser source.

46. The system of any of items 41-45, wherein the wavelength of thefirst light beam ranges from 600 nm to 2 μm.

47. The system of any of items 41-46, wherein the wavelength of thesecond light beam ranges from 600 nm to 2 μm.

48. The system of any of items 41-47, wherein the first light sourcecomprises a lower power than the second light source.

49. The system of any of items 41-48, wherein the first light source isseparate from the second light source.

50. The system of any of items 41-48, wherein the first light source andthe second light source comprise a single source operable at selectablepower levels.

51. The system any of items 41-50, wherein the second light beam fromthe second light source is operable to ablate melanin at a resolution ofless than 10 μm in the image plane.

52. The system of any of items 41-51, wherein the second light beam fromthe second light source is operable to ablate melanin at a resolution ofless than 1 μm in the image plane.

53. The system of any of items 41-52, wherein the second light beam fromthe second light source is operable to ablate melanin at a resolution ofless than 500 nm in the image plane.

54. The system of items 41-53, wherein the second light beam from thesecond light source is operable to ablate a single grain of melanin.

55. The system of any of items 41-54, wherein the detector comprises aphoton detector.

56. The system of any of items 41-55, wherein the detector comprises aphotomultiplier tube, avalanche photodiodes, a spectrometer, a CCD imagearray detector, or a CMOS photodiode array detector.

57. The system of any of items 41-56, further comprising a scanningsystem operative to scan the light beams from the first light source andthe second light source across the image plane.

58. The system of any of items 41-57, wherein the scanning systemcomprises one or two scanning mirrors disposed to scan in orthogonaldirections.

59. The system of any of items 41-57, wherein the scanning mirrorscomprise one or more of a galvanometer mirror scanner or a rotatingpolygonal mirror scanner.

60. The system of any of items 41-59, further comprising a supportdisposed to support the region of tissue.

61. The system of any of items 41-60, wherein the support comprises astage movable with respect to the image plane within the region oftissue, whereby fluorescence of melanin in multiple image planes can beinduced and at least a portion of the melanin in multiple image planescan be ablated.62. The system of any of items 41-61, wherein the objective lensassembly is movable with respect to the image plane within the region oftissue, whereby fluorescence of the melanin in multiple image planes canbe induced and at least a portion of the melanin in multiple imageplanes can be ablated.63. The system of any of items 41-62, further comprising one or moreoptical components disposed on the optical path to transmit the firstlight beam and the second light beam to the image plane.64. The system of any of items 41-63, wherein the objective lensassembly and the first light source are selected to provide a lightintensity at a focal area sufficient to induce fluorescence of melaninin the image plane.65. The system of any of item 41-64, wherein the objective lens assemblyand the second light source are selected to provide a light intensity ata focal area sufficient to ablate melanin in the image plane.66. The system of any of items 41-65, further comprising a controller incommunication with the objective lens assembly, the first light source,the second light source and the detector, wherein the controller isoperative to store detected fluorescence signals from the melanin in theimage plane and to control the second light source to ablate melanin atlocations in the tissue corresponding to the detected fluorescencesignals.67. The system of any of items 41-66, wherein the controller isoperative to scan the first light source over the region of tissue toinduce the stepwise multi-photon fluorescence, to generate a mapspecifying areas of the detected fluorescence in the region, and to movethe second light source to the areas of the detected fluorescencespecified in the map.68. The system of any of items 41-67, wherein the controller isoperative to move the first light source to a further region of tissue,store detected fluorescence signals from the melanin in the furtherregion, and control the second light source to ablate at least a portionof the melanin from which the fluorescence is detected in the furtherregion.69. The system of any of items 41-68, wherein the controller isoperative to control repetition of the steps of inducing stepwisemulti-photon fluorescence in melanin, detecting the fluorescence fromthe melanin, and ablating at least a portion of the melanin from whichthe fluorescence is detected at a new region of tissue.70. The system of any of items 41-69, wherein the controller isoperative to monitor fluorescence from the region after ablation todetermine whether ablation has been completed.71. The system of any of items 41-70, wherein at least the objectivelens assembly and a portion of the optical path from the first lightsource and the second light source are housed within a hand-held device.72. The method of item 38, wherein the melanocytic lesion is selectedfrom the group consisting of benign nevus and malignant melanoma.73. The method of item 38, wherein the congenital or acquiredhyperpigmentation or melanin deposition is selected from the groupconsisting of melasma, hyperpigmentation from chronic nutritionaldeficiency, congenital pigment deposition, Addison's disease,McCune-Albright syndrome, sun damage, solar lentigo, deposition sundamage, ephelides, freckle, café au lait macule, nevus of Ota, nevus ofIto, post inflammatory hyperpigmentation, nevus spilus, seborrheickeratosis, blue nevus, Becker's nevus, uneven skin tone, and vitiligo.74. The method of item 38, wherein the other skin discoloration frommelanin deposition is selected from the group consisting of depositionassociated with metals or mercury poisoning, and skin discoloration dueto a side effect from drug usage.

DESCRIPTION OF THE DRAWINGS

The invention will be more fully understood from the following detaileddescription taken in conjunction with the accompanying drawings inwhich:

FIG. 1 is a schematic illustration of simultaneous and stepwise photonexcitation;

FIG. 2 is a block diagram of an embodiment of a melanin ablation system;

FIG. 3 is a block diagram of a controller of a melanin ablation system;

FIG. 4 is a schematic illustration of an objective lens assembly of amelanin ablation system;

FIG. 5 is a schematic illustration of an embodiment of a hand-helddevice for a melanin ablation system;

FIG. 6 is a flow chart of an embodiment of a method of melanin ablation;

FIG. 7 is a flow chart of a further embodiment of a method of melaninablation;

FIG. 8 is a schematic diagram of an embodiment of an optical layout of amelanin ablation system;

FIG. 9A is a brightfield image of a melanin block in sepia skin beforeablation;

FIG. 9B is a brightfield image of the melanin block of FIG. 9A afterablation;

FIGS. 10A-10D are a group of images of a melanin block in which FIG. 10Ais a brightfield image of the melanin block before ablation; FIG. 10B isa brightfield image after ablation of a letter Z in the melanin block;FIG. 10C is an enlarged image of the ablated area of FIG. 10B; and FIG.10D is an SMPAF image of the melanin block after ablation;

FIG. 11 is a schematic illustration of an ablation pattern for theletter Z in FIG. 10;

FIG. 12A is a brightfield image of a melanin block before ablation;

FIG. 12B is a brightfield image of the melanin block of FIG. 12A afterthe letters Z and L have been ablated in the melanin block, each letterhaving a size of ˜40×50 μm;

FIG. 13 is a comparison of melanin SMPAF activation threshold in air,nitrogen, and water for synthetic eumelanin, sepia eumelanin,Fe-saturated melanin, and EDTA washed (iron removed) melanin;

FIGS. 14A-14B are graphs of (a) melanin EPR signals before and afteractivation, and (b) normalization of the EPR signals of (a);

FIGS. 15A-15D illustrate photomicrographs of a white hair and a blackhair from a human subject in which FIG. 15A is a brightfield image, FIG.15B is a confocal reflectance microscopy (CRM) image, FIG. 15C is aconventional multi-photon fluorescence microscopy (MPFM) image, and FIG.15D is an SMPAF image with excitation wavelength of 785 nm;

FIGS. 16A-16B are schematic illustrations of an energy diagramdemonstrating in FIG. 16A simultaneous excitation, and in FIG. 16Bstepwise excitation using three-photon excitation as an example;

FIG. 17 is a schematic profile of a pulsed laser, in which T is thepulse width and T_(L) is the period; and

FIG. 18 is a schematic illustration of (a) an experimental setup of anoptical configuration to provide an optical delay, and (b) a profile ofthe output laser beam.

DETAILED DESCRIPTION OF THE INVENTION

This application incorporates by reference the entire disclosure of U.S.Provisional Application No. 62/020,459 filed on Jul. 3, 2014, entitled“The Stepwise Multi-Photon Activated Fluorescence Guided SelectiveAblation of Melanin.”

The present invention provides a method and system that utilizes thestepwise multi-photon activated fluorescence (SMPAF) of melanin to guidethe ablation of melanin in human or animal skin or other tissue. Themethod and system can be used to treat melanin-related skin diseases andconditions with a high precision. A continuous-wave (CW) laser lightsource can be used to induce fluorescence and provide ablation at lowcost.

Typically, multi-photon fluorescence involves the simultaneousabsorption of photons to excite an electron from the ground state to theexcited state, which requires the use of a laser pulsed for extremelyshort intervals, on the order of femtoseconds, at high instantaneouspower to achieve a high photon flux. Fluorescence of melanin, however,can occur with a step-wise multi-photon excitation process, in whichphotons are absorbed individually and sequentially and the electron isexcited step-wise from the ground state to an intermediate state orstates before reaching the state at which fluorescence occurs. See FIG.1.

More particularly, enhanced melanin fluorescence can be induced by astep-wise multi-photon activated fluorescence (SMPAF) process. Anactivation step to induce the melanin SMPAF signal can employ radiationranging from the visible to the near infrared (NIR), from 600 nm to 2μm. Melanin fluorescence can shift depending on the wavelength of theexcitation source. In one example, using a 1505 nm laser has resulted ina peak at approximately 960 nm. Fluorescence has been activated usinglow laser power, with intensities on the order of 10⁵ to 10′ W/cm².SMPAF can also detect melanin without background interference from otherbiological components.

Stepwise multi-photon activated fluorescence (SMPAF) differs fromsimultaneous two-photon excitation of fluorescence in several ways. Thestep-wise process involves real intermediate excitation states, whilethe simultaneous process lacks real intermediate states. SMPAF can occurwith excitation intensities that are two or more orders of magnitudelower than simultaneous excitation processes to obtain the samepopulation density of fluorescence. The intensity needed to activate themulti-step fluorescence process is lower than for simultaneousfluorescence. Thus, the step-wise multi-photon activation process canemploy a continuous wave (CW) laser, rather than a pulsed laser,substantially reducing the cost. The lifetimes of the intermediatestates and the excited states of activated melanin is calculated andestimated using rate equations are discussed in more detail below.

Referring to FIGS. 2-3, one embodiment of a system 10 for melaninablation employs a light transmission source 20 operable at multiplepower levels, a lower level 22 for inducing fluorescence of the melaninfor detecting the location of the melanin in a sample or region oftissue, and a higher level 24 for subsequent ablation of the melaninonce detected. The system also includes a support 30, such as a stage orother surface, for securely holding the sample or region of tissuecontaining melanin during the steps of inducing and detectingfluorescence and the subsequent ablation of melanin. An objective lensassembly 40 is provided on an optical path 12 from the light source 20to the region of tissue to focus the light beam on an image plane withinthe region of tissue. Other optical components 50 can be provided on theoptical path 12 for transmission of the light beam from the light source20 to the region of tissue, depending on the configuration of thesystem. A scanning system 60 can be provided for scanning the light beamover the image plane. A stepwise multi-photon activated fluorescence(SMPAF) detector 70 is also provided to receive fluorescence signalsemitted from melanin present in the region of tissue. A partiallyreflective, partially transmissive mirror 72 or beam splitter can beused to divert the fluorescence signals that travel back along theoptical path to the SMPAF detector while allowing the light beam fromthe light source(s) to pass through to the region of tissue. Acontroller 80 can be provided in communication with the various systemcomponents to direct their operations.

In one embodiment, the light transmission source 20 can be a coherent orlaser light source, which can comprise two separate laser sourcesoperable at different power levels or one laser source switchablebetween different power levels. The or each laser source can be acontinuous wave laser source or a pulsed laser. Notably, a continuouswave laser source can suitably be used for SMPAF melanin detection andablation, as described above. Suitable wavelengths for inducingfluorescence and for ablation can range from 600 nm to 2 μm. Thewavelengths of the low power source 22 and the high power source 24 canbe the same or different. Laser sources can include, for example andwithout limitation, ruby lasers, alexandrite lasers, diode lasers, andNd:YAG lasers. The controller 80 controls operation of both the lowerpower level and the higher power level sources, for example, by turningeach source on or off at the appropriate times or switching power levelsof a single source. In other embodiments, a non-coherent source, forexample, a zenon lamp, can be used.

The objective lens assembly 40 is provided to focus the light beam on animage plane within the region of tissue. The objective lens assemblydetermines the focal area or resolution on the image plane. Resolutioncan be specified as the diameter of the focal area. In some embodiments,the objective lens can achieve a resolution in the image plane of lessthan 10 μm. In some embodiments, a resolution can be achieved of lessthan 1 μm in the image plane. In still further embodiments, a resolutioncan be achieved of less than 500 nm in the image plane. In still furtherembodiments, a resolution can be the size of a particle or grain ofmelanin. Melanin grain size diameters can range from 30 nm to 400 nm.Objective lens assemblies capable of achieving these resolutions arecommercially available, such as, for example, some of the various CFIseries objectives available from Nikon Corporation of Japan.

The laser power necessary to induce fluorescence and subsequently ablatethe melanin is determined by a laser intensity at the focal plane orimage plane. Referring to the schematic illustration in FIG. 4, theintensity is the power P divided by the area A of the laser beam in anyparticular image plane. (FIG. 4 schematically illustrates a focal pointfor purposes of illustrating the intensity at a focal or image plane; itwill be appreciated that, in practice, the focal point has a finitearea, or resolution, in the image plane.) The light transmission source20 and the objective lens assembly 40 can be selected, or coordinated bythe controller 80, to provide a power level from the light source(s)sufficient to achieve a minimum threshold intensity for inducingfluorescence of melanin and for ablation of melanin in the image plane.With the small resolutions achievable with the objective lens assembly,the system is able to achieve intensities sufficient to ablate melaninwith no or minimal collateral damage to adjacent tissue. The system alsocan in principle ablate melanin without damaging melanocytes. In someembodiments, the intensity can be on the order of 10⁵ to 10⁷ W/cm².Deeper penetration or thicker tissue can require a higher intensity dueto energy loss.

Melanin can be present at various depths in a region of tissue, such ashuman or animal skin. Accordingly, the system can move the image planeto various depths. Each image plane can have a thickness (dimension inthe depth dimension) ranging from 300 nm to 4 μm. Use of near infraredwavelengths by the light source(s) in particular allows a greater depthof penetration. The depth of penetration into the sample can range fromthe surface to the full depth of a dermis layer of skin, for example, 6mm, or more. In some embodiments, the depth of penetration can rangefrom the surface to 500 μm; in other embodiments, the depth ofpenetration can range from the surface to 6 mm. In some embodiments, thedepth of penetration can be as deep as 6 mm, as deep as 7 mm, as deep as8 mm, as deep as 9 mm, or as deep as 1 cm.

The penetration depth of the image plane can be adjusted in any suitablemanner. In some embodiments, the objective lens assembly 40 can be movedor optical components within the objective lens assembly can be adjustedto move the image plane in the Z-direction within the region of tissue.In other embodiments, the system can employ as the support 30 a stagethat can be moved in the depth direction (a Z-direction) each time a newimage plane is to be imaged.

Various additional optical components 50 are provided on the opticalpath to transmit the light beam from the light source or sources to thesample containing the melanin. The optical components can include,without limitation, beam expanders; collimating lenses; telescope orrelay lenses; filters, such as shortpass filters, longpass filters, andpolarizing filters; mirrors, such as partially transmitting mirrors anddichroic mirrors; beam splitters; quarter wave plates; and the like,depending on the application. In some embodiments, the system can beimplemented as a portable or hand-held device. A hand-held device mayrequire the use of a more compact optical configuration than a largerstationary device or a microscope. In some embodiments, a portion of thesystem, such as the objective lens assembly 40 and a portion of theoptical path 12 from the first and second light sources 22, 24 can behoused in a hand-held device.

The system also includes a scanning system 60, in communication with thecontroller 80, to provide scanning of the laser beam in the X and Ydirections over the image plane. Any suitable scanning system can beused, such as two galvanometer scanners, one for scanning in the Xdirection and one for scanning in the Y direction. Other scanningsystems can be used, such as one galvanometer mirror tiltable in boththe X and Y directions, two rotating polygonal mirror arrays or acombination of a rotating polygonal mirror and galvanometer mirror. Byscanning an appropriate low level laser beam across an area in an imageplane containing melanin, melanin present within the area in the imageplane can be induced to fluoresce.

The SMPAF detector 70 can be any suitable detector capable of detectinglight in the spectrum emitted during melanin fluorescence. Any suitablephoton detector can be used. Such detectors include, without limitation,a photomultiplier tube, avalanche photodiodes, a spectrometer, a CCDimage array detector, or a CMOS photodiode array detector. A mirror 72,such as a partially reflecting, partially transmitting mirror ordichroic mirror, can be located in the optical path to divert thefluorescence signal from melanin to the detector. The SMPAF detector canalso be in communication with the controller 80 to provide data to thecontroller regarding locations from which fluorescence signals arereceived. The controller can also be in communication with the scanningsystem to control the scanning and thereby map the locations of receivedfluorescence signals with their locations of origin within the region oftissue.

In some embodiments, the system for melanin ablation can be implementedas a hand-held device. For example, referring to FIG. 5, a hand-helddevice can house the objective lens assembly 40 and other opticalcomponents in a housing 15. The housing can include a support surface 31adjacent an exit of the objective lens assembly 40 to maintain theregion of tissue stationary with respect to the objective lens assembly.The hand-held device can be connected via a cable 17, such as a fiberoptic cable, to a base unit 17 that can house other components, such asthe controller and light transmission source.

In some embodiments, the system can be implemented with a stage forsupporting a sample or region of tissue. In some embodiments, the stagecan be movable in two (X-Y or in-plane) dimensions parallel to the imageplane. In other embodiments, the stage can be movable in three (X-Y-Z)dimensions to provide out-of-plane motion as well. Motion of the stagecan be provided in any suitable manner, such as with one or more steppermotors or piezoelectric motors in communication with the controller. Anyother suitable mechanical, electrical, or electromechanical components,such as gearing and linkages, can be provided to effect movement of thestage.

FIG. 6 illustrates an embodiment of a method of melanin ablation. Thelow power level light source 22 is directed to a first point in an imageplane (step 101) to transmit light to induce SMPAF of melanin at thatpoint (step 102). If SMPAF is detected (step 103), then the melanin atthat point is ablated using the high power level light source (step104). The low power level light source is moved to another point in theimage plane (step 105) and the inducing and detecting steps (102, 103)are repeated. If melanin is detected, the ablating step (step 104) isperformed. Optionally, the system can check for SMPAF immediately aftereach ablation step to determine if ablation is sufficiently completebefore moving to the next point in the image plane.

FIG. 7 illustrates a further embodiment of a method of melanin ablation.The low power level light source is scanned over an image plane (step121), for example, in a raster pattern. If melanin is detected (step122), a map is generated of the image plane indicating wherefluorescence is detected (step 123). The map is used to designate areasof melanin ablation (step 124). Then the high power level light sourceis moved over the image plane to ablate melanin in the designated areas(step 125). Optionally, to monitor the ablation, the low power levellight source can be scanned over the image plane again to detect SMPAF(step 126). Once ablation in the image plane is satisfactorilycompleted, the objective lens or stage is adjusted to move the focalarea to the next image plane (step 127).

Referring now to FIG. 8, one embodiment of an optical layout withoptical components 250 and scanning system 260 for use in a system forthe detection and ablation of melanin is illustrated. This system alsoincludes a brightfield mode for viewing a sample or region of tissue andobtaining images thereof. A continuous wave laser 220 is provided,controlled by a diode controller, to serve as the illumination sourcefor the SMPAF (path 282). The laser beam is first expanded andcollimated by a beam expander 251. A two-dimensional scanning system 260is provided. In one embodiment, a first galvanometer scanner 261 scansthe beam along the X-axis. A first telescope lens assembly 252 is usedas a relay. A second galvanometer scanner 262 scans the beam along theY-axis. A second telescope lens 253 assembly is used as a beam expanderas well as a relay. A switchable mirror 272 is utilized for switchingbetween the brightfield mode and the SMPAF mode. The SMPAF signals arecollected by an objective lens system 240, and delivered to a SMPAFphotomultiplier tube 270 through a longpass dichroic mirror 254 (path284). A halogen lamp 255 serves as the illumination source of thebrightfield mode (path 286). The brightfield images are collected by acamera system 256, such as a CCD camera. In this embodiment, the imagesreaching the camera system are mirrored images; thus, the images aremirrored again by software.

Referring to FIG. 3, the controller 80 can include memory 82 and aprocessing unit(s) 84 and can be in communication with various input andoutput devices 86 to allow an operator to use the system. For example,the controller can store in memory detected fluorescence signals fromthe melanin in each of the image planes and can include stored driversor routines with instructions for controlling operation of the elementsof the system.

In some embodiments, the controller 80 is operative to scan the firstlight source over an image plane in a region of tissue to induce thestepwise multi-photon fluorescence of melanin and to generate a mapspecifying areas of the detected fluorescence in the image plane. Themap can be defined by, for example, a pixel array in which pixels wherefluorescence has been detected are identified. The controller is furtheroperative to move the second light source to the areas of the detectedfluorescence specified in the map to ablate melanin at those locations.The second light source can be moved in any suitable pattern to ablatethe melanin. The controller is operative to move the first light sourceover a further region of tissue to induce fluorescence, store detectedfluorescence signals from the melanin in the further region, and controlthe second light source to ablate at least a portion of the melanin fromwhich the fluorescence is detected in the further region. The furtherregion of tissue can be an image plane located at a different depth inthe region of tissue, in which case the controller can be operative toadjust the objective lens assembly or the stage.

In some embodiments, the controller is operative to monitor thefluorescence signal from the region after ablation to determine whetherablation is complete. In some applications, such as skin lightening, itmay not be necessary to ablate all of the melanin detected in theregion. The controller can be operative to control the amount of melaninablated, for example, by ablating a predetermined percentage of detectedmelanin or by monitoring the amount of melanin detected after ablation.

The controller can be part of a computer system that executesprogramming for controlling the system for ablating melanin as describedherein. The computing system can be implemented as or can include acomputing device that includes a combination of hardware, software, andfirmware that allows the computing device to run an applications layeror otherwise perform various processing tasks. Computing devices caninclude without limitation personal computers, work stations, servers,laptop computers, tablet computers, mobile devices, hand-held devices,wireless devices, smartphones, wearable devices, embedded devices,microprocessor-based devices, microcontroller-based devices,programmable consumer electronics, mini-computers, main frame computers,and the like.

The computing device can include a basic input/output system (BIOS) andan operating system as software to manage hardware components,coordinate the interface between hardware and software, and manage basicoperations such as start up. The computing device can include one ormore processors and memory that cooperate with the operating system toprovide basic functionality for the computing device. The operatingsystem provides support functionality for the applications layer andother processing tasks. The computing device can include a system bus orother bus (such as memory bus, local bus, peripheral bus, and the like)for providing communication between the various hardware, software, andfirmware components and with any external devices. Any type ofarchitecture or infrastructure that allows the components to communicateand interact with each other can be used.

Processing tasks can be carried out by one or more processors. Varioustypes of processing technology can be used, including a single processoror multiple processors, a central processing unit (CPU), multicoreprocessors, parallel processors, or distributed processors. Additionalspecialized processing resources such as graphics (e.g., a graphicsprocessing unit or GPU), video, multimedia, or mathematical processingcapabilities can be provided to perform certain processing tasks.Processing tasks can be implemented with computer-executableinstructions, such as application programs or other program modules,executed by the computing device. Application programs and programmodules can include routines, subroutines, programs, drivers, objects,components, data structures, and the like that perform particular tasksor operate on data.

The computing device includes memory or storage, which can be accessedby the system bus or in any other manner. Memory can store controllogic, instructions, and/or data. Memory can include transitory memory,such as cache memory, random access memory (RAM), static random accessmemory (SRAM), main memory, dynamic random access memory (DRAM), andmemristor memory cells. Memory can include storage for firmware ormicrocode, such as programmable read only memory (PROM) and erasableprogrammable read only memory (EPROM). Memory can include non-transitoryor nonvolatile or persistent memory such as read only memory (ROM), harddisk drives, optical storage devices, compact disc drives, flash drives,floppy disk drives, magnetic tape drives, memory chips, and memristormemory cells. Non-transitory memory can be provided on a removablestorage device. A computer-readable medium can include any physicalmedium that is capable of encoding instructions and/or storing data thatcan be subsequently used by a processor to implement embodiments of themethod and system described herein. Physical media can include floppydiscs, optical discs, CDs, mini-CDs, DVDs, HD-DVDs, Blu-ray discs, harddrives, tape drives, flash memory, or memory chips. Any other type oftangible, non-transitory storage that can provide instructions and/ordata to a processor can be used in these embodiments.

The computing device can include one or more input/output interfaces forconnecting input and output devices to various other components of thecomputing device. Input and output devices can include, withoutlimitation, keyboards, mice, joysticks, microphones, displays, monitors,scanners, speakers, and printers. Interfaces can include universalserial bus (USB) ports, serial ports, parallel ports, game ports, andthe like.

The computing device can access a network over a network connection thatprovides the computing device with telecommunications capabilities.Network connection enables the computing device to communicate andinteract with any combination of remote devices, remote networks, andremote entities via a communications link. The communications link canbe any type of communications link, including without limitation a wiredor wireless link. For example, the network connection can allow thecomputing device to communicate with remote devices over a network,which can be a wired and/or a wireless network, and which can includeany combination of intranet, local area networks (LANs), enterprise-widenetworks, medium area networks, wide area networks (WANs), the Internet,or the like. Control logic and/or data can be transmitted to and fromthe computing device via the network connection. The network connectioncan include a modem, a network interface (such as an Ethernet card), acommunication port, a PCMCIA slot and card, or the like to enabletransmission of and receipt of data via the communications link.

The computing device can include a browser and a display that allow auser to browse and view pages or other content served by a web serverover the communications link. A web server, server, and database can belocated at the same or at different locations and can be part of thesame computing device, different computing devices, or distributedacross a network. A data center can be located at a remote location andaccessed by the computing device over a network. The computer system caninclude architecture distributed over one or more networks, such as, forexample, a cloud computing architecture.

Example 1

In one example, using an optical layout substantially as indicated inFIG. 8, a sepia sample was obtained from a piece of squid skin. Thelaser source was a 975 nm CW laser. The sample was placed between acover glass and a microscope slide. FIG. 9A is a photomicrograph of aregion of the sample showing several melanin blocks. One of the melaninblocks was fully ablated in one image plane, as shown in FIG. 9B. Thelaser power used to ablate the melanin block was estimated to be 39.2mW. Note that only the melanin in the image plane has been ablated; toablate all the melanin in this block, the image plane would need to bemoved vertically with respect to the melanin block.

Example 2

In a further example, micrometer resolution of melanin ablation wasdemonstrated by performing a partial ablation of a melanin block. FIGS.10A-10D are a group of photomicrographs illustrating a block of melaninbefore and after ablation. The sample containing the melanin wasobtained from a piece of squid skin. The letter “Z” having dimensions25×35 μm was ablated in a melanin block. FIG. 10A is a brightfield imageof the sepia skin before ablation. FIG. 10B is a brightfield image ofthe same location after ablation. FIG. 10C is an enlarged image of thecircled area in FIG. 10B. FIG. 10D is a SMPAF image of the circulatearea after ablation. The ablated letter Z is best seen in FIG. 10D. Thelaser power used to ablate the melanin was estimated to be 62.98 mW. Thelaser trajectory used to ablate the letter Z is illustrated in FIG. 11.

Example 3

In a still further example, a partial ablation was performed on amelanin block to further demonstrate micrometer resolution. The lettersZ and L were ablated in a block of melanin in a sepia skin from a squid.FIG. 12A is a brightfield image of the sepia skin before laser ablation.FIG. 12B is a brightfield image of the same location after laserablation. The letters Z and L, each of ˜40×50 m in size, were created bypartially ablating the melanin block at the center. The laser power atthe sample was measured to be 34.5 mW.

Various additional details regarding the SMPAF process are described byreference to FIGS. 13, 14A, 14B, 15A-15D, 16A, 16B, and 18. Regardingthe activation process, a large photon density above the activationthreshold is used to activate melanin SMPAF. The activation threshold ofmelanin SMPAF can vary by the type of melanin as well as the surroundingenvironment. In some embodiments, the activation threshold is on theorder of 10⁵ to 10⁶ W/cm². After activation, SMPAF signals can bedetected below the activation threshold. Thus, the laser power can bedecreased after activation for purposes of detecting melanin. MelaninSMPAF can be activated and excited using either pulsed or CW lasers. Theactivation time can vary among melanin particles. In some embodiments,the activation time can be less than 60 s. The average activation timedecreases as laser power increases. The activation threshold of varioustypes of melanin was compared, as indicated in FIG. 13. The activationthreshold was determined by increasing the input laser power step bystep, with a pause of at least 1 min at each step, until SMPAF signalswere detected.

The activation of melanin SMPAF may be caused in part by thedissociation of metal ions or the selective degradation ofiron-containing melanin. A comparison of melanin electron paramagneticresonance (EPR, also known as electron spin resonance (ESR)) of melaninbefore and after activation was performed. See FIGS. 14A, 14B. Theintensity of the EPR signal decreased after activation, while the shapesof the signals remained the same. This comparison indicates those freeradicals were removed from the melanin during the activation step.

Many biological components emit auto-fluorescence under a pulsed laser,causing background signals. Melanin, however, emits SMPAF signals underthe activation process described herein, which provides for a highspecificity in detecting melanin in skin compared to other biologicalcomponents. FIGS. 15A-15D illustrate several photomicrographs of a whitehair and a black hare from a human subject. In the brightfield image,FIG. 15A, the white hair and the black hair are readily distinguishable,although melanin cannot be detected. The confocal reflectance microscopy(CRM) image, FIG. 15B, provides details of the physical structure, butmelanin also cannot be detected. The conventional multi-photonfluorescence microscopy (MPFM) image, FIG. 15C, provides fluorescencesignals from both melanin and other biological components. The SMPAFimage, FIG. 15D, shows fluorescence signals from melanin with highspecificity while lacking background signals from other biologicalcomponents.

Stepwise Excitation vs. Simultaneous Excitation

As mentioned previously in this chapter, the commonly known multi-photonfluorescence is usually a simultaneous excitation process, whereas themulti-photon activated fluorescence of melanin is a stepwise excitationprocess, which is similar to the simultaneous excitation process, exceptthat all the intermediate states between the excited state and theground state are real states. In simultaneous excitation, lifetime ofthe virtual states is estimated to be ˜10⁻¹⁶ s. The lifetime of the realstates are much longer (usually ˜10⁻⁹ s).

The energy diagrams shown in FIGS. 16A and 16B follow the rate equationsbelow:

$\begin{matrix}{{{\frac{d}{d\; t}N_{1}} = {{R_{01} \cdot {I(t)} \cdot ( {N_{0} - N_{1}} )} - {{R_{12} \cdot I}{(t) \cdot ( {N_{1} - N_{2}} )}} - \frac{N_{1}}{T_{1}}}},} & {{Equation}\mspace{14mu} 1} \\{{{\frac{d}{d\; t}N_{2}} = {{{R_{12} \cdot I}{(t) \cdot ( {N_{1} - N_{2}} )}} - {{R_{23} \cdot I}{(t) \cdot ( {N_{2} - N_{3}} )}} - \frac{N_{2}}{T_{2}}}},} & {{Equation}\mspace{14mu} 2} \\{\mspace{79mu}{{{\frac{d}{d\; t}N_{3}} = {{{R_{23} \cdot I}{(t) \cdot ( {N_{2} - N_{3}} )}} - {{R_{3} \cdot I}{(t) \cdot N_{3}}} - \frac{N_{3}}{T_{3}}}},}} & {{Equation}\mspace{14mu} 3}\end{matrix}$where N₀, N₁, N₂, and N₃ are the electron population density of State 0(ground state), 1, 2, and 3 (excited state) respectively. Here, wesuppose N₀ is constant. R₀₁, R₁₂, and R₂₃ are the transition rates fromState 0 to State 1, State 1 to State 2, and State 2 to State 3respectively. R₃ is the decay rate of the excited state. T₁, T₂, and T₃are the lifetime of State 1, 2, and 3 respectively. I(t) is theintensity of the input laser.

To populate electrons from State 0 to State 3, we need to have:N ₀ >>N ₁ >>N ₂ >>N ₃.  Equation 4

Therefore, Equation 1-Equation 3 can be simplified as:

$\begin{matrix}{{{\frac{d}{d\; t}N_{1}} = {{{R_{01} \cdot I}{(t) \cdot N_{0}}} - \frac{N_{1}}{T_{1}}}},} & {{Equation}\mspace{14mu} 5} \\{{{\frac{d}{d\; t}N_{2}} = {{{R_{12} \cdot I}{(t) \cdot N_{1}}} - \frac{N_{2}}{T_{2}}}},} & {{Equation}\mspace{14mu} 6} \\{{\frac{d}{d\; t}N_{3}} = {{R_{23} \cdot I}{(t) \cdot {N_{2}.}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

a) Pulsed Laser

Suppose the input laser is a pulsed laser, with pulse width τ, periodT_(L), and intensity I(t) as shown in FIG. 17.

-   -   i) Simultaneous Excitation

The pulse width of an exemplary laser (for example, a Tsunami laser fromSpectra Physics) is ˜10⁻¹³ s, which is much longer than the lifetime ofvirtual states, but shorter than that of the excited states (usually˜10⁻⁹ s). Then we haveT ₁ ,T ₂ <<τ<<T ₃.  Equation 8

At t∈(0, τ), I(t)>>0, from Equation 5, we have:

$\begin{matrix}{{N_{1} = {{C_{1} \cdot e^{- \frac{t}{T_{1}}}} + {R_{01} \cdot N_{0} \cdot e^{- \frac{t}{T_{1}}} \cdot {\int{{e^{\frac{t}{T_{1}}} \cdot {I(t)} \cdot d}\; t}}}}},} & {{Equation}\mspace{14mu} 9}\end{matrix}$where C₁ is a constant.

Since

$\begin{matrix}{{{\int{{e^{\frac{t}{T_{1}}} \cdot {I(t)} \cdot d}\; t}} = {{T_{1} \cdot e^{\frac{t}{T_{1}}} \cdot {I(t)}} - {T_{1} \cdot {\int{e^{\frac{t}{T_{1}}}{d\lbrack {I(t)} \rbrack}}}}}},} & {{Equation}\mspace{14mu} 10}\end{matrix}$we have

$\begin{matrix}{N_{1} = {{{C_{1} \cdot e^{- \frac{t}{T_{1}}}} + {R_{01} \cdot N_{0} \cdot T_{1} \cdot {I(t)}} - {R_{01} \cdot N_{0} \cdot T_{1} \cdot e^{- \frac{t}{T_{1}}} \cdot {\int{e^{\frac{t}{T_{1}}}{d\lbrack {I(t)} \rbrack}}}}} \approx {R_{01} \cdot N_{0} \cdot T_{1} \cdot {{I(t)}.}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Here, as from Equation 8, T₁<<τ, hence

${C_{1} \cdot e^{- \frac{t}{T_{1}}}} \approx 0.$

To prove that

$\begin{matrix}{{{R_{01} \cdot N_{0} \cdot T_{1} \cdot {I(t)}}\operatorname{>>}{R_{01} \cdot N_{0} \cdot T_{1} \cdot e^{- \frac{t}{T_{1}}} \cdot {\int{e^{\frac{t}{T_{1}}}{d\lbrack {I(t)} \rbrack}}}}},} & {{Equation}\mspace{14mu} 12}\end{matrix}$

we need to prove

$\begin{matrix}{{{I(t)}\operatorname{>>}{e^{- \frac{t}{T_{1}}} \cdot {\int{e^{\frac{t}{T_{1}}}{d\lbrack {I(t)} \rbrack}}}}},} & {{Equation}\mspace{14mu} 13}\end{matrix}$

which is to prove

$\begin{matrix}{{{I(t)} \cdot e^{\frac{t}{T_{1}}}}\operatorname{>>}{\int{e^{\frac{t}{T_{1}}} \cdot \frac{d\lbrack {I(t)} \rbrack}{dt} \cdot {{dt}.}}}} & {Equation14}\end{matrix}$

Since

$\begin{matrix}{{{{I(t)} \cdot e^{\frac{t}{T_{1}}}} = {{\int{\frac{d\lbrack {{I(t)} \cdot e^{\frac{t}{T_{1}}}} \rbrack}{dt}{dt}}} = {{\int{e^{\frac{t}{T_{1}}}{\frac{d\lbrack {I(t)} \rbrack}{dt} \cdot {dt}}}} + {\frac{1}{T_{1}} \cdot {\int{e^{\frac{t}{T_{1}}} \cdot {I(t)} \cdot {dt}}}}}}},} & {{Equation}\mspace{14mu} 15}\end{matrix}$

to prove Equation 14, we only need to prove

$\begin{matrix}{{\frac{1}{T_{1}} \cdot {\int{e^{\frac{t}{T_{1}}} \cdot {I(t)} \cdot {dt}}}}\operatorname{>>}0.} & {{Equation}\mspace{14mu} 16}\end{matrix}$

Equation 16 is true since

$\frac{1}{T_{1}},e^{\frac{t}{T_{1}}},$

and I(t) are all >>0.

We rewrite Equation 11 below as:N ₁ ≈R ₀₁ ·N ₀ ·T ₁ ·I(t).  Equation 17

Similarly, from Equation 6 and Equation 17, we have

$\begin{matrix}\begin{matrix}{N_{2} =} & {{C_{2} \cdot e^{- \frac{t}{T_{2}}}} + {R_{12} \cdot e^{- \frac{t}{T_{2}}} \cdot {\int{e^{\frac{t}{T_{2}}} \cdot {I(t)} \cdot N_{1} \cdot {dt}}}}} \\{\approx} & {{C_{2} \cdot e^{- \frac{t}{T_{2}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot T_{1} \cdot}} \\ & {e^{- \frac{t}{T_{2}}} \cdot {\int{e^{\frac{t}{T_{2}}} \cdot \lbrack {I(t)} \rbrack^{2} \cdot {dt}}}} \\{\approx} & {{R_{12} \cdot R_{01} \cdot N_{0} \cdot T_{1} \cdot T_{2} \cdot {I(t)}^{2}},}\end{matrix} & {{Equation}\mspace{14mu} 18}\end{matrix}$where C₂ is a constant.

From Equation 7 and Equation 18, we haveN ₃ =R ₂₃ ·∫I(t)·N ₂ ·dt≈R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀ ·T ₁ ·T ₂ ∫I(t)³·dt.  Equation 19

At t∈(τ, T_(L)), I(t)=0, though there is no input photons, State 3 ispopulated. Emission will occur following the equation below:

$\begin{matrix}{{\frac{d}{dt}N_{3}} = {- {\frac{N_{3}}{T_{3}}.}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

Therefore

$\begin{matrix}{{N_{3} = {{- {\int_{\tau}^{T_{L}}{\frac{N_{3}}{T_{3}}{dt}}}} = {N_{3}^{0} \cdot e^{- \frac{t - \tau}{T_{3}}}}}},} & {{Equation}\mspace{14mu} 21}\end{matrix}$where N₃ ⁰ is the electron population density of State 3 at time τ,which isN ₃ ⁰ =R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀ ·T ₁ ·T ₂ ·∫I(t)³ dt=R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀·T ₁ ·T ₂·(I(t)³)·T _(L).  Equation 22

Therefore, the detected fluorescence signal is

$\begin{matrix}\begin{matrix}{{F \propto \langle {N_{3}(t)} \rangle} =} & {{\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{N_{3}\mspace{14mu}{dt}}}} = {\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{N_{3}^{0} \cdot}}}} \\ & {{e^{- \frac{t - \tau}{T_{3}}}{dt}} = {\frac{N_{3}^{0}}{T_{L}} \cdot T_{3} \cdot ( {1 - e^{- \frac{T_{L} - \tau}{T_{3}}}} )}} \\{\approx} & {\frac{N_{3}^{0}}{T_{L}} \cdot {T_{3}.}}\end{matrix} & {{Equation}\mspace{14mu} 23}\end{matrix}$

By combining Equation 22 and Equation 23, we haveF∝

N ₃(t)

≈R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀ ·T ₁ ·T ₂ ·T ₃ ·

I(t)³

,  Equation 24which meansF∝

I ³

.  Equation 25

-   -   i) Stepwise excitation

In stepwise excitation, the laser pulse width is much shorter than thelifetime of the intermediate states (usually ˜10⁻⁹ s). Then Equation 8is changed toτ<<T ₁ ,T ₂ T ₃.  Equation 26

At t∈(0,τ), I(t)>>0, Equation 1-Equation 3 can be simplified as:

$\begin{matrix}{{{\frac{d}{dt}N_{1}} = {R_{01} \cdot {I(t)} \cdot N_{0}}},} & {{Equation}\mspace{14mu} 27} \\{{{\frac{d}{dt}N_{2}} = {R_{12} \cdot {I(t)} \cdot N_{1}}},} & {{Equation}\mspace{14mu} 28} \\{{\frac{d}{dt}N_{3}} = {R_{23} \cdot {I(t)} \cdot {N_{2}.}}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

From Equation 27N ₁ =R ₀₁ ·N ₀ ·∫I(t)dt.  Equation 30

From Equation 28 and Equation 30,N ₂ =R ₁₂ ·I(t)·R ₀₁ ·N ₀ ·∫I(t)·[∫I(t)dt]·dt=½·R ₁₂ ·R ₀₁ ·N₀·[∫I(t)dt]².  Equation 31

From Equation 29 and Equation 31,

$\begin{matrix}\begin{matrix}{N_{3} = {R_{23} \cdot {I(t)} \cdot \frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int{{I(t)} \cdot \lbrack {\int{{I(t)}\mspace{14mu}{dt}}} \rbrack^{2} \cdot {dt}}}}} \\{= {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\lbrack {\int{{I(t)}\mspace{14mu}{dt}}} \rbrack^{3}.}}}\end{matrix} & {{Equation}\mspace{14mu} 32}\end{matrix}$

At t∈(τ, T_(L)), I(t)=0, Equation 1-Equation 3 can be simplified as:

$\begin{matrix}{{{\frac{d}{dt}N_{1}} = {- \frac{N_{1}}{T_{1}}}},} & {{Equation}\mspace{14mu} 33} \\{{{\frac{d}{dt}N_{2}} = {- \frac{N_{2}}{T_{2}}}},} & {{Equation}\mspace{14mu} 34} \\{{\frac{d}{dt}N_{3}} = {- {\frac{N_{3}}{T_{3}}.}}} & {{Equation}\mspace{14mu} 35}\end{matrix}$

From Equation 33,

$\begin{matrix}{{N_{1} = {{- {\int_{\tau}^{T_{L}}{\frac{N_{1}}{T_{1}}{dt}}}} = {N_{1}^{0} \cdot e^{- \frac{t - \tau}{T_{1}}}}}},} & {{Equation}\mspace{14mu} 36}\end{matrix}$where N₁ ⁰ is the electron population density of State 1 at time τ,which isN ₀ ¹ =R ₀₁ ·N ₀∫₀ ^(τ) I(t)dt=R ₀₁ ·N ₀

I(t)

·T _(L).  Equation 37

Similarly, from Equation 34 and Equation 37,

$\begin{matrix}{{N_{2} = {N_{2}^{0} \cdot e^{- \frac{t - \tau}{T_{2}}}}},} & {{Equation}\mspace{14mu} 38}\end{matrix}$whereN ₂ ⁰=½·R ₁₂ ·R ₀₁ ·N ₀·[∫₀ ^(τ) I(t)dt]²=½ R ₁₂ ·R ₀₁ ·N ₀ ·

I(t)

² ·T _(L) ².  Equation 39

From Equation 35 and Equation 39,

$\begin{matrix}{{N_{3} = {N_{3}^{0} \cdot e^{- \frac{t - \tau}{T_{3}}}}},} & {{Equation}\mspace{14mu} 40}\end{matrix}$whereN ₃ ⁰=⅙·R ₂₃ ·R ₁₂ ·N ₀·[∫₀ ^(τ) I(t)dt]³=⅙ R ₂₃ ·R ₁₂ ·N ₀ ·

I(t)

³ ·T _(L) ³.  Equation 41

Therefore, the detected fluorescence signal

                                     Equation  42 $\begin{matrix}{{F \propto \langle {N_{3}(t)} \rangle} = {{\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{N_{3}{dt}}}} = {{\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{{N_{3}^{0} \cdot e^{- \frac{t - \tau}{T_{3}}}}{dt}}}} = {\frac{N_{3}^{0}}{T_{L}} \cdot T_{3} \cdot}}}} \\{( {1 - e^{- \frac{T_{L} - \tau}{T_{3}}}} )} \\{\approx {\frac{N_{3}^{0}}{T_{L}} \cdot T_{3} \cdot ( {1 - e^{- \frac{T_{L}}{T_{3}}}} )}} \\{{= {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \langle {I(t)} \rangle^{3} \cdot T_{L}^{2} \cdot T_{3} \cdot ( {1 - e^{- \frac{T_{L}}{T_{3}}}} )}},}\end{matrix}$

which meansF∝N ₃ ∝

I

³.  Equation 43

a) CW Laser

Assuming that the system has reached equilibrium under the exposure ofCW laser with intensity I, we have

$\begin{matrix}{{\frac{d}{dt}N_{1}} = {{\frac{d}{dt}N_{2}} = {{\frac{d}{dt}N_{3}} = 0.}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$

Therefore, Equation 5-Equation 7 can be simplified as:N ₁ =R ₀₁ ·I·N ₀ ·T ₁,  Equation 45N ₂ =R ₁₂ ·I·N ₁ ·T ₂ =R ₁₂ ·R ₀₁ ·I ² ·N ₀ ·T ₂ ·T ₁,  Equation 46N ₃ =R ₂₃ ·I·N ₂ ·T ₃ =R ₂₃ ·R ₁₂ ·R ₀₁ ·I ³ ·N ₀ ·T ₃ ·T ₂ ·T₁,  Equation 47

which meansF∝N ₃ ∝I ³.  Equation 48

Equation 47 is also consistent with Equation 24.

b) Conclusion

Although Equation 25 and Equation 43 appear similar to each other, thedifference is significant under a femtosecond pulsed laser. Take theTsunami laser as an example, with pulsed width ˜10⁻¹³ s and period 12.5ns,

$\begin{matrix}{\frac{\langle I^{3} \rangle}{\langle I \rangle^{3}} \sim {10^{10}.}} & {{Equation}\mspace{14mu} 49}\end{matrix}$

Therefore, stepwise excitation can be readily achieved using a CW laser,whereas simultaneous excitation requires a pulsed laser.

Intermediate States of Melanin SMPAF

Use Equation 47 divided by Equation 42, we have

$\begin{matrix}{\frac{N_{3}^{CW}}{\langle N_{3}^{pulsed} \rangle} = {\frac{R_{23} \cdot R_{12} \cdot R_{01} \cdot I^{3} \cdot N_{0} \cdot T_{3} \cdot T_{2} \cdot T_{1}}{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \langle {I(t)} \rangle^{3} \cdot T_{L}^{2} \cdot T_{3} \cdot ( {1 - e^{- \frac{T_{L}}{T_{3}}}} )} = {\frac{6 \cdot T_{2} \cdot T_{1}}{( {1 - e^{- \frac{T_{L}}{T_{3}}}} ) \cdot T_{L}^{2}}.}}} & {{Equation}\mspace{14mu} 50}\end{matrix}$

the signal strength of melanin SMPAF signal is the same order when usingCW or pulsed mode of the Tsunami laser. (J. Kerimo, M. Rajadhyaksha andC. A. DiMarzio, “Enhanced Melanin Fluorescence by Stepwise Three-photonExcitation,” Photochemistry and Photobiology 87(5), 1042-1049 (2011))For the Tsunami laser, T_(L)˜10⁻⁸ s, suppose T₁≈T₂, then we haveT ₁ ≈T ₂˜10⁻⁹ s.  Equation 51which is consistent with our previous estimate.

To further understand the lifetime of the intermediate states of melaninSMPAF, an optical delay was designed as shown in FIG. 18(a). The laserbeam coming from the pulsed laser is separated into two braches by abeam splitter, BS1. The longer path created a delay of Δt between thetwo paths. A tunable neutral density filter is able to control theintensity of the longer path. The longer and shorter paths are thenmerged by a second beam splitter, BS2, to create a new beam.

The profile of the new beam is shown in FIG. 18 part B. Two pulses arecreated at each period T_(L).

At t∈(0, τ), I(t)=I₁(t>>0, from Equation 30-Equation 32,N ₁ =R ₀₁ ·N ₀ ·∫I ₁(t)dt,  Equation 52N ₂=½·R ₁₂ ·R ₀₁ ·N ₀·[∫I ₁(t)dt]²,  Equation 53N ₃=⅙·R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀[∫I ₁(t)dt]³.  Equation 54

At t∈(τ, τ+Δt), I(t)=0, from Equation 36-Equation 41

$\begin{matrix}{{N_{1} = {N_{1}^{0} \cdot e^{- \frac{t - \tau}{T_{1}}}}},} & {{Equation}\mspace{14mu} 55}\end{matrix}$whereN ₁ ⁰ =R ₀₁ ·N ₀∫₀ ^(τ) I ₁(t)dt;  Equation 56

$\begin{matrix}{{N_{2} = {N_{2}^{0} \cdot e^{- \frac{t - \tau}{T_{2}}}}},} & {{Equation}\mspace{14mu} 57}\end{matrix}$

whereN ₂=½·R ₁₂ ·R ₀₁ ·N ₀·[∫₀ ^(τ) I ₁(t)dt]²,  Equation 58

$\begin{matrix}{{N_{3} = {N_{3}^{0} \cdot e^{- \frac{t - \tau}{T_{3}}}}},} & {{Equation}\mspace{14mu} 59}\end{matrix}$

whereN ₃ ⁰=⅙·R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀[∫₀ ^(τ) I ₁(t)dt]³.  Equation 60

When t∈(τ+Δt, 2τ+Δt), I(t)=I ₂(t). Uset′=t−(τ+Δt).  Equation 61

Then t′∈(0,τ). From Equation 5, we have:

$\begin{matrix}{{N_{1} = {{C_{1} \cdot e^{- \frac{t^{\prime}}{T_{1}}}} + {R_{01} \cdot N_{0} \cdot e^{- \frac{t^{\prime}}{T_{1}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{1}}} \cdot {I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}}}},} & {{Equation}\mspace{14mu} 62}\end{matrix}$where C₁ is a constant.

For t′=0, which is t=τ+Δt, from Equation 55, Equation 56 and Equation62, we have

$\begin{matrix}{{N_{1}( {t^{\prime} = 0} )} = {N_{1}^{01} = {{N_{1}^{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}}} = {{{e^{- \frac{\Delta\; t}{T_{1}}} \cdot R_{01} \cdot N_{0}}{\int_{0}^{\tau}{{I_{1}(t)}{dt}}}} = {C_{1}.}}}}} & {{Equation}\mspace{14mu} 63}\end{matrix}$

Therefore

$\begin{matrix}{N_{1} = {{{R_{01} \cdot N_{0}}{\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{{\Delta\; t} + t^{\prime}}{T_{1}}}}}}} + {R_{01} \cdot N_{0} \cdot e^{- \frac{t^{\prime}}{T_{1}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{1}}} \cdot {I_{2}( t^{\prime} )} \cdot {{dt}^{\prime}.}}}}}} & {{Equation}\mspace{14mu} 64}\end{matrix}$

Since t′<τ<<T₁, we have

$\begin{matrix}{N_{1} \approx {{{R_{01} \cdot N_{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}}}{\int_{0}^{\tau}{{I_{1}(t)}{dt}}}} + {R_{01} \cdot N_{0} \cdot {\int{{I_{2}( t^{\prime} )} \cdot {{dt}^{\prime}.}}}}}} & {{Equation}\mspace{14mu} 65}\end{matrix}$

Similarly, From Equation 6, we have:

$\begin{matrix}{N_{2} = {{C_{2} \cdot e^{- \frac{t^{\prime}}{T_{2}}}} + {R_{12} \cdot e^{- \frac{t^{\prime}}{T_{2}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{2}}} \cdot {I_{2}( t^{\prime} )} \cdot N_{1} \cdot {{dt}^{\prime}.}}}}}} & {{Equation}\mspace{14mu} 66}\end{matrix}$

For t′=0, from Equation 57, Equation 58 and Equation 66,

$\begin{matrix}{{N_{2}( {t^{\prime} = 0} )} = {N_{2}^{01} = {{N_{2}^{0} \cdot e^{- \frac{\Delta\; t}{T_{2}}}} = {{e^{- \frac{\Delta\; t}{T_{2}}} \cdot N_{2}^{0}} = {{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2}} = C_{2\;.}}}}}} & {{Equation}\mspace{14mu} 67}\end{matrix}$

Therefore, from Equation 65, Equation 66 and Equation 67

                                     Equation  68$N_{2} = {{{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{{\Delta\; t} + t^{\prime}}{T_{2}}}} + R_{12} + {e^{- \frac{t^{\prime}}{T_{2}}} \cdot {\int{{e^{\frac{t^{\prime}}{T_{2}}} \cdot I_{2}}{( t^{\prime} ) \cdot \lbrack {{{R_{01} \cdot N_{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}}}{\int_{0}^{\tau}{{I_{1}(t)}{dt}}}} + {R_{01} \cdot N_{0} \cdot {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}}}} \rbrack \cdot {dt}^{\prime}}}}}} = {{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{{\Delta\; t} + t^{\prime}}{T_{2}}}} + R_{12} + {R_{01} \cdot N_{0} \cdot e^{- \frac{t^{\prime}}{T_{2}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{2}}} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack \cdot {I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot e^{- \frac{t^{\prime}}{T_{2}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{2}}} \cdot \lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack \cdot {I_{2}( t^{\prime} )} \cdot {{dt}^{\prime}.}}}}}}$

Since t′<τ<<T₁, T₂, we have

                                     Equation  69${N_{2} \approx {{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack \cdot {\int{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int{\lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack \cdot {I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}}}} = {{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack \cdot {\int{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{2}.}}}$

From Equation 7, we have:

$\begin{matrix}{N_{3} = {{C_{3} \cdot e^{- \frac{t^{\prime}}{T_{3}}}} + {R_{23} \cdot e^{- \frac{t^{\prime}}{T_{3}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{3}}} \cdot {I_{2}( t^{\prime} )} \cdot N_{2} \cdot {{dt}^{\prime}.}}}}}} & {{Equation}\mspace{14mu} 70}\end{matrix}$

For t′=0, from Equation 59, Equation 60 and Equation 70, we have

$\begin{matrix}{{N_{3}( {t^{\prime} = 0} )} = {N_{3}^{01} = {{N_{3}^{0} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} = {{e^{- \frac{\Delta\; t}{T_{3}}} \cdot \frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3}} = {C_{3}.}}}}} & {{Equation}\mspace{14mu} 71}\end{matrix}$

Therefore,

                                     Equation  72$N_{3} = {{{e^{- \frac{\Delta\; t}{T_{3}}} \cdot \frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{t^{\prime}}{T_{3}}}} + {R_{23} \cdot e^{- \frac{t^{\prime}}{T_{3}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{3}}} \cdot {I_{2}( t^{\prime} )} \cdot \{ {{\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}}} + {R_{12} \cdot R_{01} \cdot N_{0} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack \cdot {\int{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{2}}} \} \cdot {dt}^{\prime}}}}} = {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}} \cdot e^{- \frac{t^{\prime}}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot e^{- \frac{t^{\prime}}{T_{3}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{3}}} \cdot {I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot e^{- \frac{t^{\prime}}{T_{3}}} \cdot {\int{e^{\frac{t^{\prime}}{T_{3}}} \cdot {I_{2}( t^{\prime} )} \cdot {\int{{I_{2}( t^{\prime} )}{{dt}^{\prime} \cdot {dt}^{\prime}}}}}}}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot e^{- \frac{t^{\prime}}{T_{3}}} \cdot {\int{{e^{\frac{t^{\prime}}{T_{3}}} \cdot I_{2}}{( t^{\prime} ) \cdot \lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{2} \cdot {{dt}^{\prime}.}}}}}}}$

Since t′<τ<<T₁, T₂, we have

${ \mspace{650mu}{{{Equation}\mspace{14mu} 73}{N_{3} \approx {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot {\int{{I_{2}( t^{\prime} )} \cdot {\int{{I_{2}( t^{\prime} )}{{dt}^{\prime} \cdot {dt}^{\prime}}}}}}}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int{{I_{2}( t^{\prime} )} \cdot \lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{2}}}}}}} \} \cdot {dt}^{\prime}} = {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{2}}}}} + {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\lbrack {\int{{I_{2}( t^{\prime} )}{dt}^{\prime}}} \rbrack^{3}.}}}$

When t∈(2τ+Δt, T_(L)), I(t)=0. From Equation 7

$\begin{matrix}{{N_{3} = {N_{3}^{02} \cdot e^{- \frac{t^{\prime} - \tau}{T_{3}}}}},} & {{Equation}\mspace{14mu} 74}\end{matrix}$where

                                     Equation  75$N_{3}^{02} = {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{2}}}}} + {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{3}.}}}$

Therefore, the detected fluorescence signal

                                     Equation  76${F \propto \langle {N_{3}(t)} \rangle} = {{\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{N_{3}\;{dt}}}} = {{\frac{1}{T_{L}} \cdot ( {{\int_{\tau}^{{\Delta\; t} + \tau}{{N_{3}^{0} \cdot \; e^{- \frac{t - \tau}{T_{3}}}}{dt}}} + {\int_{\tau}^{T_{L} - {\Delta\; t} - \tau}{{N_{3}^{02} \cdot e^{- \frac{t - \tau}{T_{3}}}}{dt}}}} )} = {\frac{T_{3}}{T_{L}} \cdot {\lbrack {{N_{3}^{0} \cdot ( {1 - e^{- \frac{\Delta\; t}{T_{3}}}} )} + {N_{3}^{02} \cdot ( {1 - e^{- \frac{T_{L} - {\Delta\; t} - {2\;\tau}}{T_{3}}}} )}} \rbrack.}}}}$

Therefore, the detected fluorescence signal

                                     Equation  77${F \propto \langle {N_{3}(t)} \rangle} = {{\frac{1}{T_{L}} \cdot {\int_{0}^{T_{L}}{N_{3}\;{dt}}}} = {{\frac{1}{T_{L}} \cdot ( {{\int_{\tau}^{{\Delta\; t} + \tau}{{N_{3}^{0} \cdot \; e^{- \frac{t - \tau}{T_{3}}}}{dt}}} + {\int_{\tau}^{T_{L} - {\Delta\; t} - \tau}{{N_{3}^{02} \cdot e^{- \frac{t - \tau}{T_{3}}}}{dt}}}} )} = {\frac{T_{3}}{T_{L}} \cdot {\lbrack {{N_{3}^{0} \cdot ( {1 - e^{- \frac{\Delta\; t}{T_{3}}}} )} + {N_{3}^{02} \cdot ( {1 - e^{- \frac{T_{L} - {\Delta\; t} - {2\;\tau}}{T_{3}}}} )}} \rbrack.}}}}$

Again t′<τ<<T₁, T₂, then

$\begin{matrix}{\langle {N_{3}(t)} \rangle \approx {\frac{T_{3}}{T_{L}} \cdot {\lbrack {N_{3}^{0} - {N_{3}^{0} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + N_{3}^{02} - {N_{3}^{02} \cdot e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}}} \rbrack.}}} & {{Equation}\mspace{14mu} 78}\end{matrix}$

From Equation 60 and Equation 75,

                                     Equation  79${\langle {N_{3}(t)} \rangle \approx {\frac{T_{3}}{T_{L}} \cdot \{ {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3}} - {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{2}}}}} + {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{3}} - {\{ {{\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{2}}}}} + {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{3}}} \} \cdot e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}}} \}}} = {\frac{R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot T_{3}}{T_{L}} \cdot {\{ {{\frac{1}{6} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3}} + {\frac{1}{2} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{{dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{2}}}}} + {\frac{1}{6} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{3}} - {\{ {{\frac{1}{6} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{3} \cdot e^{- \frac{\Delta\; t}{T_{3}}}} + {\frac{1}{2} \cdot \lbrack {\int_{0}^{\tau}{{I_{1}(t)}{dt}}} \rbrack^{2} \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}}} + {\frac{1}{2} \cdot {\int_{0}^{\tau}{{I_{1}(t)} \cdot {dt} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{2}}}} + {\frac{1}{6} \cdot \lbrack {\int_{0}^{\tau}{{I_{2}( t^{\prime} )} \cdot {dt}^{\prime}}} \rbrack^{3}}} \} \cdot e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}}} \}.}}$

By definition

$\begin{matrix}{{\langle {I_{1}(t)} \rangle = {\frac{1}{T_{L}} \cdot {\int_{0}^{\tau}{{I_{1}(t)}{dt}}}}},} & {{Equation}\mspace{14mu} 80} \\{\langle {I_{2}(t)} \rangle = {\frac{1}{T_{L}} \cdot {\int_{0}^{\tau}{{I_{2}( t^{\prime} )}{{dt}^{\prime}.}}}}} & {{Equation}\mspace{14mu} 81}\end{matrix}$

From Equation 79, Equation 80 and Equation 81, we have

                                     Equation  82$\langle {N_{3}(t)} \rangle = {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot T_{3} \cdot T_{L}^{2} \cdot {\lbrack {{\langle {I_{1}(t)} \rangle^{3} \cdot ( {1 - e^{- \frac{T_{L}}{T_{3}}}} )} + {3 \cdot \langle {I_{2}(t)} \rangle^{2} \cdot \langle {I_{2}(t)} \rangle \cdot e^{- \frac{\Delta\; t}{T_{2}}} \cdot ( {1 - e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}} )} + {3 \cdot \langle {I_{2}(t)} \rangle \cdot \langle {I_{2}(t)} \rangle^{2} \cdot e^{- \frac{\Delta\; t}{T_{1}}} \cdot ( {1 - e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}} )} + {\langle {I_{2}(t)} \rangle^{3} \cdot ( {1 - e^{- \frac{T_{L} - {\Delta\; t}}{T_{3}}}} )}} \rbrack.}}$

Let T_(L)>>T₃, and T_(L)−Δt>>T₃, then

                                     Equation  83$F \propto \langle {N_{3}(t)} \rangle \approx {\frac{1}{6} \cdot R_{23} \cdot R_{12} \cdot R_{01} \cdot N_{0} \cdot T_{3} \cdot T_{L}^{2} \cdot {( {\langle {I_{1}(t)} \rangle^{3} + {3 \cdot \langle {I_{1}(t)} \rangle^{2} \cdot \langle {I_{2}(t)} \rangle \cdot e^{- \frac{\Delta\; t}{T_{2}}}} + {3 \cdot \langle {I_{1}(t)} \rangle \cdot \langle {I_{2}(t)} \rangle^{2} \cdot e^{- \frac{\Delta\; t}{T_{1}}}} + \langle {I_{1}(t)} \rangle^{3}} ).}}$

If we block the orange path, I₂(t)=0, then

N ₃ ¹

=⅙R ₂₃ ·R ₁₂ ·R ₀₁ ·N ₀ ·T ₃ ·T _(L) ² ·

I ₁(t)

³.  Equation 84

Equation 84 is consistent with our previous work (Equation 42 whenT_(L)>>T₃).

Use Equation 83 divide by Equation 84, we have

$\begin{matrix}{\frac{F_{3}^{{1\&}2}}{F_{3}^{1}} = {\frac{\langle N_{3}^{{1\&}2} \rangle}{\langle N_{3}^{1} \rangle} = {\frac{\begin{matrix}{\langle {I_{1}(t)} \rangle^{3} + {3 \cdot \langle {I_{1}(t)} \rangle^{2} \cdot \langle {I_{1}(t)} \rangle \cdot e^{- \frac{\Delta\; t}{T_{2}}}} + {3 \cdot \langle {I_{1}(t)} \rangle \cdot}} \\{{\langle {I_{1}(t)} \rangle^{2} \cdot e^{- \frac{\Delta\; t}{T_{1}}}} + \langle {I_{1}(t)} \rangle^{3}}\end{matrix}}{\langle {I_{1}(t)} \rangle^{3}}.}}} & {{Equation}\mspace{14mu} 85}\end{matrix}$

Therefore, by varying I₂(t) using the neutral density filter andmeanwhile monitoring the fluorescence signal, we can solve T₁ and T₂,which are the lifetime of the intermediate states.

The method and system can be used for the treatment of melanin-relateddiseases and conditions in subjects in need thereof. Melanin-relateddiseases can include, without limitation, melanocytic lesions,congenital or acquired hyperpigmentation/melanin deposition, and otherskin discoloration due to deposition, for example, associated withmetals (such as mercury poisoning) or as a side effect from drug usage.Melanocytic lesions can include, for example, benign nevi and malignantmelanoma. Hyperpigmentation/melanin deposition can include or arisefrom, for example, melasma; chronic nutritional deficiency; congenitalpigment deposition, such as Addison's disease or McCune-Albrightsyndrome; sun damage, such as solar lentigo or deposition sun damage;ephelides (freckles); café au lait macules; nevus of Ota and Ito; postinflammatory hyperpigmentations; nevus spilus; seborrheic keratoses;blue nevi; and Becker's nevus. The method and system are useful fortreatment of melanin-related diseases in sensitive areas, such as in ornear the eye, where damage to surrounding tissue is difficult to avoidusing traditional techniques. The method and system can also be used forcosmetic applications, such as correction of uneven skin tone, includingvitiligo, skin lightening, freckle removal, or hair removal. For hairremoval, the method and system can be used to ablate the melanin that ispresent in the hair shaft, thereby damaging the follicular epithelium.The method and system can be used to treat human and non-human animalsubjects.

The present method and system advantageously utilize SMPAF of melanin toguide melanin removal. The method and system can also advantageouslyutilize a low-cost continuous wave laser for melanin removal, incontrast to the more high-cost pulsed lasers used in photothermolysistechniques. It will be appreciated that a pulsed laser could, however,be used if desired.

The method and system can achieve high precision in the ablation, on theorder of 1 μm and smaller. The high power level laser of the method andsystem is able to target individual melanin particles or grains. Thehigh resolution results in no or minimal collateral damage to othercomponents of the tissue. Use of a near-infrared laser can achievedeeper penetration of the skin compared to other wavelengths used intraditional technologies.

It will be appreciated that the various features of the embodimentsdescribed herein can be combined in a variety of ways. For example, afeature described in conjunction with one embodiment may be included inanother embodiment even if not explicitly described in conjunction withthat embodiment.

The present invention has been described in conjunction with certainpreferred embodiments. It is to be understood that the invention is notlimited to the exact details of construction, operation, exact materialsor embodiments shown and described, and that various modifications,substitutions of equivalents, alterations to the compositions, and otherchanges to the embodiments disclosed herein will be apparent to one ofskill in the art.

What is claimed is:
 1. A system for ablating melanin comprising: anobjective lens assembly disposed on an optical path to focus light on animage plane within a region of tissue including melanin; a first lightsource disposed to transmit a first light beam on the optical path tothe image plane within the region of tissue, the first light beamcomprising a wavelength sufficient to induce step-wise multi-photonfluorescence of melanin in the image plane; a detector disposed toreceive a step-wise multi-photon fluorescence signal from the melanin inthe image plane returning along at least a portion of the optical path;and a second light source disposed to direct a second light beam on theoptical path to the image plane within the region of tissue, the secondlight beam comprising a wavelength and intensity sufficient to ablatemelanin in the image plane within the region of tissue.
 2. The system ofclaim 1, further comprising a controller in communication with theobjective lens assembly, the first light source, the second lightsource, and the detector, wherein the controller is operative to storedetected fluorescence signals from the melanin in the image plane and tocontrol the second light source to ablate melanin at locations in thetissue corresponding to the detected fluorescence signals.
 3. The systemof claim 1, further comprising a processor and a memory comprisinginstructions for carrying out a method comprising the steps of: inducingstepwise multi-photon fluorescence in melanin within a region of tissue;detecting the fluorescence from the melanin in the region; and ablatingat least a portion of the melanin from which the fluorescence isdetected.
 4. The system of claim 1, wherein the first light source is acontinuous wave laser and the second light source is a continuous wavelaser.
 5. The system of claim 1, wherein the second light source is acontinuous wave laser or a pulsed laser.
 6. The system of claim 1,wherein the wavelength of the first light beam is in the range from 600nm to 2 μm and the wavelength of the second light beam is in the rangefrom 600 nm to 2 μm.
 7. The system of claim 1, wherein the first lightsource operates at a lower power than the second light source.
 8. Thesystem of claim 1, wherein the first light source is separate from thesecond light source.
 9. The system of claim 1, wherein a single lightsource operable at selectable power levels serves as the first lightsource and the second light source.
 10. The system of claim 1, whereinthe second light beam is operable to ablate melanin at a resolution ofless than 10 μm in the image plane.
 11. The system of claim 1, whereinthe second light beam is operable to ablate melanin at a resolution ofless than 1 μm in the image plane.
 12. The system of claim 1, whereinthe second light beam is operable to ablate a single melanin grain. 13.The system of claim 1, wherein the detector is selected from the groupconsisting of a photon detector, a photomultiplier tube, avalanchephotodiodes, a spectrometer, a CCD image array detector, and a CMOSphotodiode array detector.
 14. The system of claim 1, further comprisinga scanning system operative to scan the light beams from the first lightsource and the second light source across the image plane.
 15. Thesystem of claim 14, wherein the scanning system comprises one or twoscanning mirrors disposed to scan in orthogonal directions.
 16. Thesystem of claim 14, wherein the scanning system comprises a galvanometermirror scanner and/or a rotating polygonal mirror scanner.
 17. Thesystem of claim 14, further comprising a controller in communicationwith the objective lens assembly, the first light source, the secondlight source, the scanner, and the detector, wherein the controller isoperative to scan the first light source over the region of tissue toinduce the stepwise multi-photon fluorescence, to generate a mapspecifying areas of the detected fluorescence in the region, and to movethe second light source to the areas of the detected fluorescencespecified in the map.
 18. The system of claim 17, wherein the controlleris operative to move the first light source to a further region oftissue, store detected fluorescence signals from the melanin in thefurther region, and control the second light source to ablate at least aportion of the melanin from which the fluorescence is detected in thefurther region.
 19. The system of claim 18, wherein the controller isoperative to control repetition of the steps of inducing stepwisemulti-photon fluorescence in melanin, detecting the fluorescence fromthe melanin, and ablating at least a portion of the melanin from whichthe fluorescence is detected at a new region of tissue.
 20. The systemof claim 17, wherein the controller is operative to monitor fluorescencefrom the region after ablation to determine whether ablation has beencompleted.
 21. The system of claim 1, further comprising a movable stagefor support of a body part comprising the region of tissue, wherein thestage is movable with respect to the image plane, and wherein the systemis configured so that fluorescence of melanin in multiple image planescan be induced and at least a portion of the melanin in multiple imageplanes can be ablated.
 22. The system of claim 1, wherein at least theobjective lens assembly and a portion of the optical path from the firstlight source and the second light source are housed within a hand-helddevice.